Two things have been pointed out:
First I can't count, we have 30 players. So we would actually only need 5 (and given we have 4 who can play if necessary, we're actually fairly close, although a few of those can only play one round).
Second, it's been mentioned that we could probably find some number of players just by looking for people willing to fill who aren't playing for tournament result.
I think a combination of these factors means it's better to aim for 35 rather than drop to 28, so I'm going to go ahead and do that. This does mean game invites will go out tomorrow, not today.